A retaining wall $30m$ high was designed to stabilize a horizontal ground surface. The back of the wall is inclined $12$ to vertical direction and can be assumed rough with interface friction angle of $30.$ The soil parameters are ${}_{cs}^{\text{'}}=30,{}_{\text{b}\text{u}\text{l}\text{k}}=19k\frac{N}{m^3},{}_{\text{s}\text{a}\text{t}}=21k\frac{N}{m^3}.$ Assume no seepage effects. Ground water table is on the ground surface.

$($a$)$ Draw a diagram to show the given wall dimensions, relevant inclinations and the direction of the active force on the wall.

$($b$)$ Calculate total lateral force on the wall.

$($c$)$ After a flood, the ground water table rises $0\mathrm{.}3m$ above the wall top surface on both sides of the wall. Calculate the lateral active force on the wall after the flood.

$($d$)$ If the weight of the wall is $(280,)k\frac{N}{m},$ is the wall safe against sliding after flooding event? Please show your calculations.